What are the divisors of 3205?

1, 5, 641, 3205

There is a total of 4 positive divisors.
The sum of these divisors is 3852.
The arithmetic mean is 963.

4 odd divisors

1, 5, 641, 3205

How to compute the divisors of 3205?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 3205 by each of the numbers from 1 to 3205 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

3205 / 1 = 3205 (the remainder is 0, so 1 is a divisor of 3205)
3205 / 2 = 1602.5 (the remainder is 1, so 2 is not a divisor of 3205)
3205 / 3 = 1068.3333333333 (the remainder is 1, so 3 is not a divisor of 3205)
...
3205 / 3204 = 1.0003121098627 (the remainder is 1, so 3204 is not a divisor of 3205)
3205 / 3205 = 1 (the remainder is 0, so 3205 is a divisor of 3205)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 3205 (i.e. 56.612719418873). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

3205 / 1 = 3205 (the remainder is 0, so 1 and 3205 are divisors of 3205)
3205 / 2 = 1602.5 (the remainder is 1, so 2 is not a divisor of 3205)
3205 / 3 = 1068.3333333333 (the remainder is 1, so 3 is not a divisor of 3205)
...
3205 / 55 = 58.272727272727 (the remainder is 15, so 55 is not a divisor of 3205)
3205 / 56 = 57.232142857143 (the remainder is 13, so 56 is not a divisor of 3205)